Session: 03-08-01: Micromechanics and Multiscale Modeling I

Paper Number: 106870

106870 - Deep Learning Driven Constitutive Model for Accelerated Crystal Plasticity Simulation 

1      Abstract

The anisotropic behaviour, hardening, deformation process and texture evolution of the polycrystalline materials are extensively demonstrated by the crystal plasticity (CP) simulation. Based on the advantages of CP simulation to understand the behaviour of materials at different length scales, it can be used more extensively in future finite element simulation in industries and academia. Some of the drawbacks associated with the CP simulation are the lack of physics based constitutive laws to improve the predictability. Another major drawback of using the CP simulation is its high computational cost because it requires the solution of time-consuming constitutive equations. Recent research has shown that we can cut back on the drawbacks of computationally costly CP simulations by introducing machine learning driven models to represent the material behaviour [1, 3, 2, 6].

The present work proposes a deep learning-based surrogate constitutive model to achieve accelerated finite element CP simulations in metallic materials. In this context, an ML model using Long Short-Term Memory (LSTM) is developed that can replace the time integration scheme for the constitutive CP model.

For the data collection, we have simulated a single crystal using unique deformation gradients (or loading cases) collected from the normal and uniform distribution method and Combinatorics. Each simulation consists of 100-time steps and features i.e., state variables and stress were collected for each step. The constitutive CP model requires the time integration of 58 independent state variables to update the stress at each step of the solution process [4]. The deformation gradients at t_n and t_n+₁ together with the stresses and state variables at t_n constitute the input for the data set, whereas the updated stress at t_n+₁ and the state variables at t_n are the outputs on which the machine learning model is trained. Following training and validation of the LSTM model, we replace the original time integration method to predict stress increments. We proceed to showcase the applicability of the model through (1) its deployment as a user subroutine (UMAT) for simulations in Abaqus commercial finite element code and (2) integrating the material model into our in-house generalized grain cluster simulation framework [5].

References

[1]     Usman Ali et al. “Application of artificial neural networks in micromechanics for polycrystalline metals”. In: INTERNATIONAL JOURNAL OF PLASTICITY 120 (Sept. 2019), pp. 205–219. ISSN: 0749-6419. DOI: 10.1016/j.ijplas. 2019.05.001.

[2]     Shravan Kotha, Deniz Ozturk, and Somnath Ghosh. “Parametrically homogenized constitutive models (PHCMs) from micromechanical crystal plasticity FE simulations, part I: Sensitivity analysis and parameter identification for Titanium alloys”. In: INTERNATIONAL JOURNAL OF PLASTICITY 120 (Sept. 2019), pp. 296–319. ISSN: 0749-6419. DOI: 10.1016/j.ijplas.2019.05.008.

[3]     Ankita Mangal and Elizabeth A. Holm. “Applied machine learning to predict stress hotspots II: Hexagonal close packed materials”. In: INTERNATIONAL JOURNAL OF PLASTICITY 114 (Mar. 2019), pp. 1–14. ISSN: 0749-6419. DOI: 10.1016/j.ijplas.2018.08.003.

[4]     Denny Dharmawan TJAHJANTO. Micromechanical modelling and simulations of transformation-induced plasticity in multiphase carbon steels. Delft University of Technology, 2008.

[5]     Sourena Yadegari, Sergio Turteltaub, and Akke SJ Suiker. “Generalized grain cluster method for multiscale response of multiphase materials”. In: Computational Mechanics 56.2 (2015), pp. 193–219.

[6]     Sheng Zhang et al. “Predicting grain boundary damage by machine learning”. In: INTERNATIONAL JOURNAL OF PLASTICITY 150 (Mar. 2022). ISSN: 0749-6419. DOI: 10.1016/j.ijplas.2021.103186.

Presenting Author: Md Nurul Abedin City, University of London

Presenting Author Biography: Nurul Abedin is a research student in the Aeronautics and Aerospace research centre. His current research aims to develop a data-driven crystal plasticity constitutive model to accelerate crystal plasticity simulation. The introduction of a data-driven model will cut back on the high computational cost and provide the solution to the crystal plasticity analysis in a shorter time.

Authors:

Md Nurul Abedin City, University of London
Sourena Yadegari Helmholtz Centre for Environmental Research - UFZ
Sathiskumar Anusuya Ponnusami City, University of London